Jean Piaget the psychologist credited with forming the theory of cognitive development in the late 1920s, created a list of mental limitations for each age. Here's what he said first graders were capable of comprehending:

First graders can understand symbols. For example, they can connect the fact that a crown can mean a king. But they still learn from concrete evidence, such as adding by counting fingers.

Most of the time you'll understand your child's logic, but she will still link together seemly unrelated things and jump to conclusions.

Reverse thinking may still be an issue. This means it will still be hard for your child to go backwards through each step to analyze a conclusion. Good luck trying to convince a child of this age that something they believe is incorrect. Even if you lay out the evidence, they'll likely have trouble following you.

First graders are still egocentric, they believe everyone sees the world as they see it. But the more you expose them to other people, especially children, the faster they'll leave this stage.

Your child will be able to tell if there is a difference in number or length or volume when comparing two objects. If you show your child two identical cups with an equal amount of water, and pour one cup into a skinny tall glass and the other cup in a short wide glass, your child will know they still have the same amount of water.

So, what are first graders capable of learning? For this question, we turn to psychologist Benjamin Bloom. In the 1950s, he led a team of researchers to create a cognitive learning guide about the process of understanding information. Each level is based on the one in front of it, similar to a staircase. Use the Piaget information to get a sense of what your child is capable of comprehending. Then take a look at Bloom's levels of learning to help you guide your child towards the next level of understanding. Bloom's levels of learning are:

Level 1: Knowledge. This is basically memorization. A child has been taught the concept and just needs to remember it. With math, for example, this is the level where he can repeat numbers.

Level 2: Comprehension. The child understands what the concept means. She realizes that a numeral stands for an amount, such as 100 stands for the amount of pennies in a dollar.

Level 3: Application. The child can come up with examples of how the concept can be used. For example, he can create his own math problems, though he won’t know the answers to the problems he creates.

Level 4: Analysis. The child can break down each idea and think of it in ways that weren't introduced. This is the level were she can solve a math problem she's never seen before.

Level 5: Synthesis. The child can apply a concept to new situations. For example, he can use addition in real life, such as adding the amount a fruit-roll-up and a juice costs to see if he has enough money to buy them both.

Level 6: Evaluation. The child judges what she's been taught and decides whether it's right or wrong. For example, she looks over the math she did and decides if the answer's correct.

By giving your child a new concept that's not beyond the mental limitations laid out by Piaget, you can watch him progress through Bloom's levels of learning. Want to give his learning a boost? Recognize where he is in the Bloom levels, then ask him a question that requires evaluation, such as asking him to judge whether learning addition is useful. This helps a child move from the rules of addition, towards thinking about how it can be used, and deciding if it's important.